NEW ALGORITHM SIMPLIFIES HEAT-EXCHANGER CALCULATIONS

Jorge Ancheyta Ruben Nares Abel Moreno Carlos G. Anaya Institute Mexicano del Petroleo Mexico City The original algorithm by Urbicain and Paloshi for the simulated operation of air-cooled heat exchangers has been modified.1 The new method reduces the running time of the programs by assuming that a row of tubes cannot belong to several passes. Simulation programs for air-cooled heat exchangers (ACHE) are useful tools for the design and operation of this type of equipment.

Dec. 16, 1991

4 min read

Jorge Ancheyta Ruben Nares Abel Moreno Carlos G. Anaya Institute Mexicano del Petroleo Mexico City

The original algorithm by Urbicain and Paloshi for the simulated operation of air-cooled heat exchangers has been modified.1

The new method reduces the running time of the programs by assuming that a row of tubes cannot belong to several passes.

Simulation programs for air-cooled heat exchangers (ACHE) are useful tools for the design and operation of this type of equipment.

Because of the wide variety of ambient temperatures occurring over the course of a year, or even a day, at refining and petrochemical facilities, a complete description of the behavior of ACHE is necessary to adapt the appropriate control.

The algorithm presented in this article is similar to Urbicain and Paloshi's, which is based on dividing the heat-transfer area of each tube into a finite number of elements.1 2 When the resulting equation system is solved, the algorithm provides an accurate profile of the equipment.

This is not the case with methods based on the global heat-transfer coefficient, calculated from terminal temperatures and average conditions and physical properties.

The equation system obtained from the energy-balance and heat-transfer rate equations is much more easily and accurately solved by the use of computers.

ALGORITHM DESCRIPTION

Let an ACHE with a total number of tubes (Nt) be arranged in Np passes with Nk rows per pass. The length (L) of a jth tube that belongs to the kth pass is divided into M equal sectors with heat-transfer areas Ai,j,k (Fig. 1).

Let a process fluid, with flow Wf and a specific heat (Cpf), flow through sector i,j,k while it is cooled from temperature Ti,j,k to Ti,l,j,k by an air stream with flow Wa, velocity Ui,j,k, and a specific heat (Cpa).

Then heat-transfer equations can be written (see nomenclature and Equations 1, 2, and 3 in Equations box) where t is the air temperature in F. and Di,i,k is the representative temperature difference.

Di,j,k can be approximated by an arithmetic mean (Equation 4) because it is a small element.3

Equations 5 and 6 are derived from Fig. 1. When Equations 4 and 6 are substituted in Equations 1, 2, and 3 and the equations are rearranged, Equations 7, 8, and 9 are obtained.

Let c and c* be defined as shown in Equations 10 and 11. Substituting Equations 7 and 8 in Equation 10 produces Equation 12, which can be simplified to give Equation 13. And substituting Equations 7 and 9 in Equation, 11 produces Equation 14, which can be simplified to give Equation 15.

Rearranging Equation 6 gives Equation 16, and substituting Equations 5 and 13 in Equation 16 gives Equation 17. And by substituting Equations 5 and 15 in Equation 4 and solving for ti,j+l,k, Equation 18 is obtained.

By letting Equation 17 equal Equation 18 and rearranging, Equation 19 is obtained, where cl is defined as in Equation 20. Equation 21 can be similarly obtained, where C2 is defined as in Equation 22.

Equations similar to 19 and 21 are obtained for each element of every tube. This results in a system of multiple, lineal equations that can be iteratively solved by the algorithm shown in Fig. 2.

COMPUTER PROGRAM

The new algorithm has been implemented in a computer program, which requires the following data to perform the simulation:

Number of tubes
Number of rows
Number of passes
Number of tube sectors
Physical properties
Manufacturing data.

The algorithm was used for the simulation of ACHE using streams from atmospheric distillation units. The main characteristics of the ACHE used in the simulation are shown in Table 1.

Fig. 3 shows the actual temperature profiles for both the fluid to be cooled and the air, through all of the ACHE, from entry to exit.

With the information generated by the simulation program, a better operational diagnosis and the appropriate equipment optimization can be obtained.

This algorithm has been satisfactorily applied in the ACHE simulation at an industrial level and in the design of air-cooled heat exchangers for Petroleos Mexicanos.

ACKNOWLEDGMENT

The authors thank Victor Briones for his helpful guidance in this project.

REFERENCES

Urbicain, H.J., and Paloshi, J., "Simulation of Air-cooled Heat Exchangers," computers and Chemical Engineering, Vol. 5, 1981, pp. 75-81.
Ancheyta, J., "Desarrollo de un programa de computo para la simulacion de cambiadores de calor enfriados por aire," ("Development of a computer program for the simulation of air cooled heat exchangers") chemical engineering BS thesis, Instituto Politecnico Nacional, Mexico, D.F., 1989.
Kern, D.O., Process Heat Transfer, McGraw-Hill Kogakuska Ltd., New York, N.Y., Tokyo, 1950.